If A = {1, 2, 3, 4}, how many elements of P(A) contain 1 but do not contain 4?
Answer and explanation
Correct answer: 4
The condition requires 1 to be included and 4 to be excluded. These two elements therefore have fixed statuses. The remaining elements 2 and 3 are unrestricted; each can be included or omitted independently. Consequently, the number of valid subsets is 2² = 4. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}. Hence option B is the only correct answer.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The condition requires 1 to be included and 4 to be excluded. These two elements therefore have fixed statuses. The remaining elements 2 and 3 are unrestricted; each can be included or omitted independently. Consequently, the number of valid subsets is 2² = 4. They are {1}, {1, 2}, {1, 3}, and {1, 2, 3}. Hence option B is the only correct answer.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
